`r(t)` parameterizes points on the first line, and `p(s)` parametrizes points on the second line. You want a point which can be parametrized by either line, so `r(t)=p(s)`

Remember that `i,j,k` are orthogonal, so a point can only be equal to another point if their number of `i` are equal (one equation), their number of `j` are equal (another equation), and their number of `k` are equal as well (third equation). So you get three equations with two variables `t,s`